Method for generating time-limited and bandpass prolate spheroidal wave function signal based on reconstruction filtering

Abstract

The invention provides a method for generating a time-limited and bandpass prolate spheroidal wave function signal based on reconstruction filtering. The time-limited and bandpass prolate spheroidal wave function signal can be generated according to a small discrete sampling value through the reconstruction filtering; and compared with the conventional method, the method can reduce the requirement on hardware memory sources, does not require bandpass filtering and is easy for engineering implementation. The method for generating the time-limited and bandpass prolate spheroidal wave function signal comprises the following steps of: determining needed sampling points through a bandpass sampling theorem; solving needed sampling values through a numerical solving algorithm; improving a signal sampling rate by more than two times of a signal maximum frequency through the reconstruction filtering; and generating continuous analog signal waveform through digital-to-analogue conversion and lowpass filtering. The method for generating the time-limited and bandpass prolate spheroidal wave function signal provided by the invention is suitable for generating the time-limited and bandpass prolate spheroidal wave function signal with a large relative bandwidth or a small relative bandwidth, and particularly suitable for generating the time-limited and bandpass prolate spheroidal wave function signal with the small relative bandwidth.

Description

A time-limited bandpass ellipsoidal wave function signal generation method based on reconstruction filtering technical field The invention relates to a method for generating an ellipsoidal wave function signal, in particular to a method for generating a time-limited bandpass ellipsoidal wave function signal based on reconstruction filtering. Background technique The ellipsoidal wave function (ProlateSpheroidalWaveFunction, PSWF) was first proposed by D.Slepian and H.O.Pollack of Bell Laboratories in the United States in the late 1950s (D.SlepianandH.O.Pollak.Prolatespheroidalwavefunctions, Fourieranalysis, anduncertainty-I.BellSyst . Tech. J., 1961, 40(1): 43-46). It has been proved to be the function with the best energy concentration and can be approximated as a function of both time limit and band limit. Due to its completeness and biorthogonality, the ellipsoidal wave function has great application potential in communication, signal processing, radar and other fields....

AI Technical Summary

Problems solved by technology

There are two main problems with this method: First, the output signal generated by this method is determined by the signal sampling value stored in the hardware, that is, the sampling rate of the input digital signal input to the digital-to-analog converter and the sampling rate of the stored signal waveform are the same and cannot be changed

Second, for the baseband ellipsoidal wave function or TB-PSWF with large relative bandwidth, it is generally easy to implement the sampling rate to satisfy the sampling theorem to sample the signal and store the sampled value, but for TB-PSWF with small relative bandwidth, If the signal is sampled according to the sampling theorem, it will cause the storage data required by the function generator to increase, the hardware complexity will be too high, and too many resources will be consumed, making it difficult to implement the project.

Therefore, using this method to generate an ellipsoidal wave function signal has the problem of engineering implementation difficulties, especially the generation of a time-limited bandpass ellipsoidal wave function signal with a small relative bandwidth is more difficult

According to the above analysis, it can be known that using the existing methods to generate time-limited bandpass ellipsoidal wave function signals has shortcomings and shortcomings such as limited application range and difficulties in engineering implementation.

Images